#ifndef STAN_MATH_PRIM_SCAL_FUN_MODIFIED_BESSEL_FIRST_KIND_HPP
#define STAN_MATH_PRIM_SCAL_FUN_MODIFIED_BESSEL_FIRST_KIND_HPP

#include <boost/math/special_functions/bessel.hpp>
#include <stan/math/prim/scal/err/check_not_nan.hpp>

namespace stan {
  namespace math {

    /**
     *
       \f[
       \mbox{modified\_bessel\_first\_kind}(v, z) =
       \begin{cases}
         I_v(z) & \mbox{if } -\infty\leq z \leq \infty \\[6pt]
         \textrm{error} & \mbox{if } z = \textrm{NaN}
       \end{cases}
       \f]

       \f[
       \frac{\partial\, \mbox{modified\_bessel\_first\_kind}(v, z)}{\partial z} =
       \begin{cases}
         \frac{\partial\, I_v(z)}{\partial z} & \mbox{if } -\infty\leq z\leq \infty \\[6pt]
         \textrm{error} & \mbox{if } z = \textrm{NaN}
       \end{cases}
       \f]

       \f[
         {I_v}(z) = \left(\frac{1}{2}z\right)^v\sum_{k=0}^\infty \frac{\left(\frac{1}{4}z^2\right)^k}{k!\Gamma(v+k+1)}
         \f]

         \f[
         \frac{\partial \, I_v(z)}{\partial z} = I_{v-1}(z)-\frac{v}{z}I_v(z)
         \f]
     *
     */
    template<typename T2>
    inline T2
    modified_bessel_first_kind(const int v, const T2 z) {
      check_not_nan("modified_bessel_first_kind", "z", z);

      return boost::math::cyl_bessel_i(v, z);
    }

  }
}

#endif
